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arXiv:cond-mat/0610828v1 [cond-mat.mtrl-sci] 30 Oct 2006

Adiabatic and Nonadiabatic Electronics of Materials

V.A. Vdovenkov1

1Moscow State Institute of Radioengineering,

Electronics and Automation (technical university)

Vernadsky ave. 78, 117454 Moscow, Russia

Abstract

Physical foundations of adiabatic and nonadiabatic electronics of materials are considered in this

article. It is shown the limitation of adiabatic approach to electronics of materials. It is shown that

nonadiabatic physical properties of solid materials (hyperconductivity, superconductivity, thermal

superconductivity and phonon drag of electrons at Debye’s temperatures of phonons) depend on

oscillations of atomic nuclei in atoms.

PACS numbers: 63.20.Kr, 63.90.+t, 71.00.00, 72.20.Pa

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I. INTRODUCTION

In modern electronics of materials, adiabatic principle mainly is used. According to

this principle, exchanging of energy between electrons and nuclei of atoms are neglected.

Today’s dominating electronics in essence is adiabatic electronics. It allows to consider

materials approximately, in adiabatic approach, and to study limited circle of their physical

properties. Development of nonadiabatic electronics, on the contrary, just begins. It takes

into the account processes of energy exchange by between electrons and nuclei of atoms, has

no basic restrictions, can reduce or remove problems of modern electronics and reveal new

physical properties of materials.

This article is devoted to analysis of physical foundations of adiabatic and nonadiabatic

electronics of materials and properties of boson-fermion fluid, arising under nonadiabatic

conditions in materials.

II. ADIABATIC ELECTRONICS OF MATERIALS

Bases of adiabatic electronics were stated by M. Born and R. Oppenheimer [1] in the

solution of Shrodinger’s stationary equation for a material HΨ = WΨ, where Hamiltonian

H contains operators of kinetic energies of electrons Te and atomic nuclei Tz , and also

the crystal potential V is dependent on sets of electrons coordinates (r) and atomic nuclei

coordinates (R) in a material. According to M. Born and R. Oppenheimer this equation is

equivalent to the following two equations:

(Te+ V )φ(r,R) = Eφ(r,R), (1)

(Tz+ E + A)Φ(R), (2)

where Te- kinetic energy of electrons’ system, W - energy of a material, φ(r,R) and Φ(R)

- wave functions for electrons system and nuclei system,

A = −

?

I

(¯ h2/MI)

?

φ∗(r,R)∇2

Rφ(r,R)dτ (3)

- adiabatic potential, MI- mass of nucleus in I −th atom, dτ - an element of the material’s

volume. Potential A describe exchange of energy between electrons and nuclei. In adiabatic

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approach, potential A is small comparing to W, and it is neglected. One believe that if A ≡ 0

then the exchange of energy between electrons and nuclei is impossible, then, one believes

that the problem of a material, stated by the equations (1, 2), is an adiabatic problem, and

electronic properties, described by the equation (1), represent a theoretical basis of adiabatic

electronics of materials. However, one can see from equations (1, 2) that upon exception of

A, a full separation of variables in these equations is not achieved, as r and R are arguments

of V . Hence, the exchange of energy between systems of electrons and nuclei in adiabatic

approach, generally speaking, is not excluded.

So, physical parameters of crystalline silicon were calculated in adiabatic approach by G.

Pastore, E. Smargiassi and F. Buda [2]. It turned out, that kinetic and potential energies

of electrons system and nuclei system deviate from average values in opposite phases to

each other with characteristic frequencies.It means that the energy exchange between

electrons and nuclei system occurs even at adiabatic conditions. Autors [2] supposed that the

greatest among the frequencies was the result of numerical method of calculation, because

at that time such frequency oscillations in crystals were not known. Later it was found

out, that this frequency coincides with the sum of two frequencies (frequency of inherent

oscillations of nucleus in silicon atom minus frequency of crystal phonon). In other words,

inherent oscillations of atomic nuclei are the fundamental property of manerials. Amplitudes

of nucleus oscillations are close to 10−12meter and consequently processes connected to

them refer to subangstroem electronics of materials. These oscillations in particular can

be an energy source for chemical reactions and for phase transitions even at extremely low

temperatures. The given result allows us to consider the adiabatic principle differently.

Adiabatic condition (A ≡ 0) means impossibility of the systematical, unidirectional stream

of energy from electrons to nuclei or from nuclei to electrons only, but does not exclude the

stream of energy periodically changing its direction.

P. Dirac [3] investigated the time-dependent Schrodinger’s equation for a crystal and

studied an opportunity of co-ordinates separation for electrons and nuclei that correspond

to adiabatic principle. He has shown that electrons and atomic nuclei move within the

effective self-consisted potential fields and generally their movements cannot be described

by equations, independent from each other. Therefore, the adiabatic principle in materials

is approximate, permitting to use it with some accuracy in certain conditions, and its ap-

plying each time requires substantiation and estimation of possible mistakes arising during

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calculation of physical quantity in such an approach.

The regular error of energy calculation for electrons in adiabatic approximation is about

< A >≈ 10−5W. It turns out to be comparable with widths of forbidden energy gapes in

many semiconductors and therefore is not always allowable. In particular, the given error

can be one of the reasons of inexact definition of deep energy levels of the local centers in

semiconductors, calculated under adiabatic approximation.

The amendments to energy of the crystal, that arise as a result of removal of potential

eq. (3) out of equation (2), according to M. Born [1], are proportional to the integer powers

of small parameter η = (m/MI)1/4<< 1 , where m- electron mass. It has given an occasion

to justify any applying of adiabatic approximation, based on smallness of η, proved to be

wrong, and, as a matter of fact, it is generally wrong in all cases. Nonadiabatic principle

and terms of its applying to materials have other physical sense.

III. CONDITIONS FOR APPLYING ADIABATIC APPROACH

It was shown by C. Herring [4] (see else: [5]), that adiabatic approach can be applied, if

Ekl>>

?

µ

¯ hωµ∆Rµ

?

d3r φ∗

k

∂

∂Rµ

φl ,(4)

where Ekl - energy of the allowed electronic transitions between states k and l , ∆Rµ -

characteristic displacement of nuclei system on frequency ωµ, µ - type of oscillations, φk

and φl- electron wave functions, ¯ h - Dirac’s constant. Adiabatic approach was studied by

A. Davidov [6] in conditions when oscillations of atomic nuclei are allowed only with one

frequency ωµ. He has come to a conclusion that adiabatic approach can be used if

Ekl>> ¯ hωµ. (5)

In other words, the adiabatic principle can be soundly applied if energy of nuclei oscillations

is less than energy of the allowed electronic transitions, for example if the energy of nuclei

oscillations is less than width of the forbidden energy gape of a semiconductor. The condition

eq. (5) is sufficient, but is not a requirement. Therefore in some cases applying of adiabatic

approximation is justified though condition eq. (5) is not carried out.

Thus, criterion of applicability of adiabatic approach in materials is not so simple, as it

quite often looks. The adiabatic principle dominates in modern physics of materials, but

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in some cases it is used unreasonably. Implications of adiabatic theories quite often appear

unproductive because of inaccurate applying of adiabatic approach. On the contrary, using

of nonadiabatic principle allows to reveal and to use new properties of materials. So, con-

ditions for applicability of adiabatic approach stated by C. Herring [4] and A. Davidov [6]

contain various types and frequencies of nuclei oscillations. Meanwhile, these nuclei oscilla-

tions (unlike oscillations of atoms or ions) are poorly investigated. It hinders well-founded

applications of adiabatic approach and halts development of nonadiabatic electronics.

IV. TYPES AND FREQUENCIES OF INHERENT OSCILLATIONS IN ATOMS

OF MATERIALS

For determining types and frequencies of nuclei inherent oscillations in atoms, it is ex-

pedient to use model of a crystal in which each atom is represented by an electron shell

and a nucleus connected with each other by quasi-elastic force. Crossection of such a three-

dimensional model by a plane containing centers of some electronic shells is shown on Fig. 1.

Electron shells with masses m” on Fig. 1 are represented as circles, nuclei with masses M′

FIG. 1: Crossection of a three-dimensional crystal model by a plane.

are represented by dark circles in centers of electronic shells. According to analytical me-

chanics the frequency of normal oscillations of a nucleus in j − th atom can be defined if to

suppose absolutely rigid all quasi-elastic connections in considered model except one quasi-

elastic connection acting between a nucleus and shell in a j − th atom. In such conditions

the oscillations of a crystal are represented by oscillations of a nucleus relatively motionless

electronic shell of j − th atom. Physically equivalent situation is established out if mass of

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an electronic shell of j−th atom m” = ∞. Hence, the frequencies spectrum of nucleus oscil-

lations is defined by known mass of a nucleus and by the potential (electric) field which hold

a nucleus in neighbourhood of the center of electron shell. This electric field is formed by

coulomb fields of nuclei and electronic shells of all atoms of a crystal. In our case it is enough

to take into account a field created only by shell of j − th atom in a neighborhood of her

center. Thus, frequencies of nucleus oscillations can be defined by considering a movement

of a nucleus in a field of a motionless environment that is in adiabatic conditions.

One can see from equation (2), that in adiabatic approach (A ≡ 0) and the potential

field acting on a nucleus, coincides with full electrons energy which for neutral atom can be

written down so:

E = Te+ EZe+ Eee+ Eex , (6)

were Te - kinetic energy of electrons, EZe - energy of electrons attraction to a nucleus,

Eee=1

energy. Electronic density χ(r) = e?Z

by electron shell in a point r, dτ - differencial of material volume where integration is

2

?Φ(r)χ(r)dτ - energy of their mutual pushing away from one enother, Eex- exchange

i=1|φi(r)|2, Φ(r) - electrostatic potential, created

carried out, e - electron carge, Z - atomic number, i - elecron number. Cyclic frequency

of harmonious oscillations of a nucleus in field, described by (6) is equal ω = (β/M)1/2,

where β - factor of the qusai-elastic force connecting a nucleus with his environment. This

frequency (ω), as is well known, is equal to a difference of the neighbor oscillations frequencies

in spectrum of quantum harmonious oscillator. We take it into account and begin the

frequencies calculation of nuclei inherent oscillations in various atoms.

In the atom of hydrogen (with atomic number Z = 1) Eee= 0, Eex= 0, Te= −EZe/2

under the virial theorem and E = EZe/2. The normalized wave function in the basic state

of hydrogen atom is Ψ1s= (1/πa3)1/2exp(−r/a), where a - Bohr’s radius. By integrating

twice the Poisson equation

1

r

d2

dr2(rΦ) =

−e

ǫ0|Ψ1s|2at boundary conditions Φ(r = ∞) = 0

and Φ(r = 0) = const we receive Φ(r) = (e/(4πǫ0a3))[(1/a + 1/r)exp(−2r/a) − 1/r] and

E = (eΦ(r))/2, where ǫ0- the electric constant. We expand E in power series, reject all

terms containing r in degrees are higher than two, and determine parabolic potential E”(r)

in which oscillations of a nucleus are harmonious. Then we calculate β = (d2E”(r)/dr2)r=0=

e2/(6πǫ0a3). Further we calculate elementary quantum of nucleus oscillations in the atom

hydrogen ¯ hω1= ¯ h?β/mp∼= 0.519eV , where mpis mass of proton.

Energy of three-dimensional quantum oscillations of a nucleus are described by the for-

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mula

E(ν) = ¯ hωZ[(1/2 + ν1) + (1/2 + ν2) + (1/2 + ν3)] ,(7)

where ν1,ν2,ν3- the oscillatory quantum numbers independently accepting values 0, 1, 2,...

In helium atom (Z = 2) two electrons in the basic state have wave functions Ψ =

φ1s(1)φ1s(2) =

1

π(Z∗/a)3exp[(−Z∗/a)(r1+ r2)], where Z∗= 2 − 5/16∼= 1.6875 - the ef-

fective charge of the nucleus not equal to 2 owing to shielding of the nucleus by elec-

trons (see ref.: [6], p. 338). We simplify the equation (6) using the property of two-

electronic systems for which Eex = −Eee/2.E = Te+ (Ze/4)Φ(r).Under the virial

theorem E = (Ze/8)Φ(r). Similarly to calculations for the hydrogen atom, we in-

tegrate Poisson equation with electronic density e|Ψ|2, determine Φ(r), and determine

β = (Ze2)(24πǫ0)−1(Z∗/a)3. Then we determine quantum of inherent oscillations of nu-

cleus in helium atom ¯ hω2=?(Ze2)(24πǫ0)−1(Z∗/a)3[2(mn+ mp)]−1 ∼= 0.402eV , where mp

and mn- masses of a proton and a neutron.

Potential field in many-electron atoms is spherically symmetric and the normalized ra-

dial wave function (Rnl) of any electronic state can be expressed through hypergeometrical

function F(b,c,d) (see reference: [6], p. 179):

Rnl= Nnl(2Zx

n

)lF(l − n + 1,2l + 2,2Zx

n

)exp(−Zx

n

) ,(8)

where Nnl =

1

(2l+1)!

?

(n+1)!

2n(n−l−1)!(2Z

n)3/2, x =

r

a, n - the principal quantum number, l - the

orbital quantum number. It follows from the (8), that electronic density about a point of

shell center is created mainly by s− electrons but densities of p−,d−,f−,... electrons are

insignificant. The density of s− electrons from L, M, N states (n = 2,3,4...) is supplemented

to density of K - electrons (n = 1). The share of density from these conditions can be

defined as squares of radial wave functions ratios: R20/R2

(R40/R10)2 ∼= 0.0123. Thus, it is visible, that the contribution to electronic density created

10∼= 0.125; (R30/R10)2 ∼= 0.037;

by 2s−, 3s−, 4s− electrons give approximately 17.4 pecent that can cause increase in

frequencies of nucleus oscillations about 5 percent. In the many-electron atoms one take

into account screening of a nucleus charge by electrons, by using an effective charge of a

nucleus Z∗∗= Z − µ, where µ = σZ1/3and values σ differ from unit a little for different

atoms: [7], vol. 2, p. 153. In view of these data the energy quantum of nucleus inherent

oscillations (quantum α - type of inherent oscillations) in the atom with number Z > 2 is

¯ hωZ= ¯ hω2

?

(Z − 5/16 − µ)3Λ(Z − µ)/Z ,(9)

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where¯ hω2 = 0.402eV - quantum of inherent oscillations of a nucleus in helium atom,

Λ = 1.2 takes into count influence of electronic s− states with quantum numbers n > 1

on value ¯ hωZ at α - type of inherent nuclei oscillations. The same result appears, when

the theorem about ellipsoid’s potentials is applied to the electron shell [8], according to the

theorem inside regular intervals the potential of a charged ellipsoid is constant. Energy

spectrum of nucleus inherent oscillation in the atom with number Z is described by the

formula (7) where ¯ hωZis calculated under the formula (9).

It is possible to write down the spherically symmetric potential field, in which the atomic

nucleus goes, as power series A[−2+x2

3−x3

3+x4

20−x5

90+...], where A = Z∗∗e2/a, x = 2r

aZ∗∗.

This function differs from parabolic dependence and because of it non-harmonic amendments

to the oscillations’ energy arise. These amendments (∆Eαν) for α - type of one-dimensional

oscillations with oscillatory numbers ν = 0,1,2 and 3 are calculated in accordance with [7],

vol. 2, p. 93, in the first and second orders of perturbation theory. As one would expect, the

greatest values of amendments relate to the oscillatory condition with ν = 3. Amendments

to energy of inherent α− type oscillations in conditions with ν = 0,1,2 and 3 for various

atoms are graphically submitted on Fig. 2. On insertion of Fig. 2 these amendments are

??

??

??

??

?

?

?

?

??

FIG. 2: Amendments (∆Eαν) to energy of α− type oscillations in conditions with ν = 0,1,2,3

depending on atoimic number Z.

submitted in the other scale for atoms under Z > 10.

The β− type of inherent oscillations, when the nucleus together with K electrons partic-

ipates in oscillations relatively other parts of the electron shell and the γ− type of inherent

oscillations when the nucleus together with K and L electrons participate in oscillations

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relatively other parts of the electron shell are also possible. Calculations have shown, that

the energy spectrum of inherent harmonious oscillations of β− and γ− types are described

by the formula (7) with corresponding value of elementary quantum of oscillations ¯ hωZfor

each of these types that can be defined under the formula (9), supposing Λ = 0.2 for β−

type of inherent oscillations and Λ = 0.05 for γ− type of inherent oscillations. The calcu-

lated and experimental values for energy quanta α−,β−,γ− types of inherent oscillations

depending on nuclear number Z, are submitted on Fig 3.

?

?

?

?

??

FIG. 3: Energy quantums of α−,β−,γ− oscillations depending on atomic number Z. Calculated

values are shown by light circles. Experimental values are shown by dark circles.

Experiments show, that inherent oscillations of α−, β− and γ− tipes are one-dimensional

oscillations. Consequently, for calculation of oscillation energy it is expedient to use the

formula linear harmonious oscillator E(ν) = (1/2 + ν)¯ hωZ, where ν = ν1 = 0,1,2... and

ν2= ν3= 0 instead of eq. (7).

It is established experimentaly, that ”zero” energy of inherent oscillations E(ν = 0) =

(1/2)¯ hωZ, and also energies (3/2)¯ hωZ and (5/2)¯ hωZ participate in optical and electrical

processes, that is typical of classical oscillations harmonious oscillators and forbidden for

free quantum oscillators. It gives the basis to consider, that oscillatios of atomic nuclei in

materials are not absolutely free and adiabatic, that meet conclusions of the quantum theory

[1, 3, 5, 6, 9] about impossibility to carry out strictly the adiabatic principle in materials. In

this connection inherent nuclei oscillations in materials show dualism of physical properties,

they manifest classical and quantum properties.

Inherent oscillations of nuclei cause strong electron-phonon interaction and stimulate

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corresponding features of physical properties of materials [10, 11, 12]. In adiabatic approach,

as we see the nuclei oscillations are possible, but an electron-phonon interaction is excluded,

though in reality this interaction accompanies inherent oscillations of nuclei. The given

contradiction exists only in adiabatic electronics and absent in nonadiabatic electronics.

V. NONADIABATIC ELECTRONICS OF MATERIALS

Nonadiabatic electronics differs in that it considers an exchange of energy between atomic

nuclei and electrons to be an important feature of materials described by the operator A

in eq. (2). It is known that for the first time researches in non-adiabatic electronics have

been undertaken more than 50 years ago by K. Huang [13], S. Pekar [14], [15] and by other

researchers who were studying the local color centers in dielectric crystals. In particular, it

has been shown, that optical and thermal properties of these centers are caused by electron-

vibrational transitions in which various oscillations of crystals can participate together with

electrons. In average, S quanta of lattice elastic oscillations of one type participate in each

such transition. According to the estimations, constant S may reach 150, but experimen-

tal values S ≤ 22. In zero-defects crystals, S << 1, that corresponds to the adiabatic

principle, and S > 1 corresponds to nonadiabatic principle. In this connection for nonadi-

abatic electronics any materials with defects of structure such as the color centers, having

the electron-vibrational nature, are important. The opportunity of electron-vibrational pro-

cesses in semiconductors in the beginning caused doubts, but later the electron-vibrational

centers (EVC) have been found in semiconductors too. It appeared that EVC and the

electron-vibrational transitions in semiconductors, associated with EVC, are the cause of

the characteristic phenomena such as phonon drag by electrons at Debye temperatures of

phonons [16], thermal superconductivity, and also the hyperconductivity representing a ver-

sion of superconductivity, that arises and exists at higher the transition temperatures than

hyperconductivity, nearby the room temperatures and higher [17]. These new properties of

semiconductors, undoubtedly, relate to the nonadiabatic electronics, because they are caused

by exchange of energy between electrons and atomic nuclei by means of electron-vibrational

transitions between stationary vibrational states of nuclei [18].

It is well known, that thermoelectric power (TEP) or Zeebeck effect in a materials include

contributions from electronic effects (the drift TEP) and electron-phonon effects (”phonon

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drag” TEP, or PDE): V = Vd+ Vph. The drift TEP (Vd) is caused by diffusion of electrons

and holes under a gradient of temperature. The PDE (Vph) exist due to dragging of electrons

and holes by phonons stream. Thermoelectric power coefficient is sum of drift thermoelectric

power coefficient and PDE coefficient: α = αd+ αph, according to [19, 20, 21]. PDE was

observed experimentally in Ge monocrystals only, at low temperatures [20, 22, 23].It

forms a band of thermoelectric power and achieves a maximum between 15 K and 30 K.

Calculations by C. Hrrring [24] predicted the decrease of PDE, observable on experience at

heating of material from 30 K up to 70 K, basically due to decreasing the interaction between

electrons and phonons. It has given the basis to wrongly believe, that PDE may exist only

at low temperatures and to count completed its researches [25]. Really, thermoelectric

power of crystalline ropes of carbon nanotubes at temperatures from 4.2 K up to 300 K in

laboratory of Nobel winner R. Smolli was presumably explained as PDE [26]. It is possible

due to strong electron-phonon interaction on EVC. Moreover, it was shown [10] that the

PDE exist in semiconductors (containing EVC) as narrow bands of temperature-dependent

thermoelectric power, located at Debye’s temperatures of various phonons of a material.

It is possible to strengthen a connection of electrons with phonons in nonmetallic materials

by introducing into them EVC. Strong interaction of electrons with phonons is provided due

to inherent oscillations of nuclei in atoms of EVC. In such conditions, mobile electrons and

holes are localised on EVC, the drift TEP decreases or disappears in general, and PDE

dominates. The moving of electrical charges in a material under action of temperature

gradient occurs basically as electron-vibrational transitions between EVC or between EVC

groups, and the value Vphdepends on speed of these transitions.

S. Pekar [27] described the intracenters nonradiative electron-vibrational transitions,

caused by elastic oscillations of a crystal at frequency ω. This theory is important for

description of PDE as it is applicable for transitions between EVC, because in each material

the EVC centers are similar each other and indiscernible. Speed of nonradiative transi-

tions of center υ(ω) from a condition k to a condition l reaches a maximum on frequency

ωm∼= Sωj, where ωj- frequency of phonon such as j, participating in transition, and it may

be expressed by the following function:

υ(ω) = υmexp

?

−(ω − ωm)2

2g”

+1

6

g

′′′(ω − ωm)3

g”3

) + ...

?

, (10)

where υm- the maximal value υ(ω), g”=?

j(qjk−qjl)2ω2

j(n∗

j+1/2), g

′′′=1

2

?

j(qjk−qjl)2ω3

j,

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(qjk−qjl) - change of equilibrium coordinates of the center, n∗

j- average value of oscillatory

quantum number. Near to a maximum of function eg. (10) value (ω − ωm) is small, power

row in a parameter exhibitors converges quickly and it is possible to be limited to the first

square-law member of the row.

Then, according to the Debye rule, we having defined a temperature of a material T =

¯ hω/k, a temperature of a material at the maximal speed of transitions Tm= ¯ hωm/k, and

Θ = ¯ h?g”/k. Believing, that the value of PDE is proportional to υ(ω), it is possible to

write down the temperature dependence of PDE as Gauss function

αph(T) = const

?

−1

2

(T − Tm)2

Θ2

?

, (11)

where const is independent of temperature. We used this function eq. (11) for approximation

contours of experimental PDE bands in containing EVC materials, by selecting values const

and θ.

Typical temperature dependence of thermoelectric power in Si monocrystal with con-

centration EVC about 1015sm−3, having rather narrow bands A, B, C, D with complex

contours, is submitted on Fig. 4. Dashed lines 1, 2, 3 on an insertion of Fig. 4 represent

Gauss curves eq. (10), corresponding to longitudinal and transverse acoustic phonons in Si.

Solid line is sum of the dashed lines. It describes a contour of a band C. It is noticed, that

PDE bands exist only in materials containing EVC and in various materials they are located

at Debye temperatures of acoustic and optical phonons of a material. It was observed in thin

epitaxial layers of materials on substrates that the PDE bands located at Debye temper-

atures of a substrate phonons. These bands are caused by electron-vibrational transitions

between EVC or between EVC groups and represent the PDE. Components of PDE bands

are well described by eq. (10) in a vicinity of their extrema. Values Θ are identical to the

contribution from any phonon type in each material and do not depend on temperature.

Values Θ for some of materials are submitted in Tab. I and in Tab. II. They definitely

reflect processes in the materials, independent from external conditions. Undoubtedly, here

there are processes of an exchange by energy between systems of electrons and atomic nuclei

which are characteristic for nonadiabatic electronics.

Contrary to for a long time ratified opinion, the received results convince us that re-

searches of PDE are not completed. The PDE researches are in the beginning of its devel-

opments, as well as nonadiabatic electronics as a whole.

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?

?

?

?

?

?

?

?

?

FIG. 4: Temperature dependency of thermoelectric power in Si, showing phonon drag effect as

bands A, B, C, D. On insertion, the dashed curves 1, 2, 3 were calculated under eq. (10). Continuous

curve is sum of the dashed curves. It approximate contour of band C.

TABLE I: Values Θ in some monocrystal materials

MaterialΘ, K MaterialΘ, K

GaAs 3.5InP 3.6

InAs4.5 GaP5.0

InSb 4.0graphite 5.0

Ge5.8 CdHgTe 14.3

Si7.5--

The hyperconductivity phenomenon differs from well-known superconductivity by details

of physical mechanism. The normalized temperature dependences of resistivity of the super-

conductor; hyperconductors are shown on Fig. 5 in the dimensionless units rs= ρ/ρsand

rg= ρ/ρg, on complex planes U and W. Materials resistivity in the beginning of transition

to the state with ρ = 0, at temperatures Tsand Tg, are denoted as ρsand ρg. Normalized

temperatures for semiconductor and superconductor are denoted ξ = T/Tsand η = T/Tg,

correspondingly, where T - Kelvin temperature.

Complex plane W can be projected to the complex plane U, for example, with the help

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TABLE II: Values Θ in some single crystal films on substrates

Material Substrate Θ, K

InAsGaAs3.5

InSbGaAs4.0

Sisapphire4.7

Carbonquartz5.0

nanotubefluorite5.0

filmsYAl garnet2.6

FIG. 5: Normalized temperature dependences of resistivity for a superconductor (rs) and for a

hyperconductor (rg) on complex planes U and W.

of transformation

U = (1 − W0)/(ReW − W0) (12)

so that the point η = 1 was projected to the point ξ = 1. The real value W0 may be

chosen so that both temperature dependences of ρ have coincided with each other with the

greatest accuracy in plane U. The basic opportunity of such superposing of the temperature

dependences ρ proves the possibility of using of the phenomenological description of super-

conductivity as well as for description of hyperconductivity. Distinctions of these materials

states with zero value ρ consist only in details of physical mechanisms.

It is possible to consider axes ξ and η as lines leaving to positive and negative infinite

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large values, closed in infinity and forming the closed contours. Temperatures in terms of ξ

are laying above the axis on Fig. 6. They relate to a superconductor. Temperatures in terms

FIG. 6: Mutual conformity between temperatures are sitting in complex plane U on axis ξ (for a

superconductor) and in complex plane W on axis η (for a hyperconductor).

η are laying below the axis of temperatures on Fig. 5. They relate to a hyperconductor.

Mutual conformity of the temperatures are sitting on the axes ξ and η, shown on Fig 6. It

is received with the help of transformation eq. (12) under W0= 2.

One can see from the Fig. 6 that temperature interval on axis ξ in plane Z, where there is a

superconductivity (0 < ξ < 1), corresponds to the interval (−∞ < η < 1) on the axis η lying

in plane U, where there is a hyperconductivity and there are negative absolute temperatures.

In other words, hyperconductors may be characterized by the negative absolute temperatures

that lie higher than indefinitely high temperatures and may be applied to the description

of physical systems with inverse population of energy levels as was shown in [28]. In our

case negative absolute temperatures should be related to the inverse population of EVC

electron-vibrational states.

Inherent oscillations of atomic nuclei influence on thermal, electric, optical and other

physical properties of nonorganic and organic materials, fullerens, carbon nanotubes and

carbon nanotube films. Inherent oscillations of nuclei, apparently, majorly define signals

propagation in nerve fibres, action of some poisons, presence and properties of aura, and also

various physical features of existence of live organisms and life in general. Thus, nonadiabatic

electronics of materials promises to be less expensive, but not less various and useful, than

existing adiabatic electronics.

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VI. DISCUSSION

Fundamental opportunities of nuclei oscillations in atoms of materials are obvious from

Schrodinger equation for a material and from adiabatic theory [1].Nevertheless, these

oscillations and the properties of materials related to them practically were not under inves-

tigation for decades, and implementations were limited by adiabatic electronics. Researches

of the materials properties related to the transitions between electronic states [9] that are

accompanied by changes of equilibrium positions or oscillations frequencies of atoms or ions

in a material were related to the nonadiabatic electronics. Thus, displacement and oscil-

lations of atoms or ions as the whole were considered, but one does not take into account

possible oscillations of nucleus in atoms though they correspond in greater degree to the

nonadiabatic principle. Modern nonadiabatic molecular mechanics, as a matter of fact, con-

sider transitions between the basic and excited electron states, and movements of nuclei,

described by classical equations of Newton. They do not take into the account the features

of interaction between moving electric charges, loses nuclei quantum features and miss new

properties of the materials caused by oscillations of atomic nuclei.

Aggregation of classical and quantum-mechanical principles in materials electronics tes-

tifies to inevitability of spreading of the classical mechanics into material microcosm what

was predicted in the beginning of the last century by far-sighted scientists.

Presently, the classical Newton mechanics is successfully applied to calculation of all

electronic quantum states in atoms of any type [29]. It proves to be the most consent with

experiment, uses the simple mathematical tool, and does not require difficult calculations.

Apparently, soon problems related to molecules, fluids and solids will be solved by classical

methods. Then electronics of materials will become classical, not split to adiabatic and

nonadiabatic electronics, because such a division exists only in wave quantum mechanics of

materials.

VII. CONCLUSION

Systems of mutually bound particles and quasi-particles, including fermions and boson,

consisting of electrons, holes, phonons and inherent oscillations of atomic nuclei, may exist

in materials. Presence of the electron-vibration centers (EVC) in materials provokes for-

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mation of such fermion-boson systems, so far as, according to the theory and experiments,

significant number of electrons, holes, phonons and inherent nuclei oscillations may have

high concentration on such centers. Though atomic nuclei practically do not migrate within

volume of a material, nevertheless, waves of inherent nuclei oscillations, as a result, cause the

fermion-boson system to be mobile as a whole, giving to it properties of a fluid. Migration

of such a fluid in a homogeneous material apparently doesn’t cause energy consumption, so

it may manifest property of superfluidity. Its movement may be considered as the mutually

bound streams of fermions and bosons. The bosons stream provides thermal superconduc-

tivity, and the fermions stream provides hyperconductivity of a material. Therefore, effects

of thermal superconductivity and hyperconductivity are linked together, as they accompany

each other. Electron-vibrational transitions between various EVC create the phonon-drag

effect on electrons at define Debye’s temperatures of material phonons or substrate phonons.

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